A type of subrings of a noetherian ring

Masayoshi Nagata

Type: Article

Publication Date: 1968-01-01

Citations: 29

DOI: https://doi.org/10.1215/kjm/1250524062

Abstract

B y a ring, we mean throughout this paper a commitative ring w ith id en tity.B y a module over a ring, w e m ean a unitary one.Let A b e a subring of a ring R such that R is a finite A-module.It is well known that if A is a noetherian ring then R is a noetherian ring.The purpose o f this paper is to prove the converse of this fact.Namely, we shall prove.

Locations

Kyoto journal of mathematics - View - PDF

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